This project aims to validate empirically a sew stimulus class account of number skill acquisition in individuals with severe to moderate mental retardation. Our analytic framework blends notions about stimulus control phenomena that have come from studies of equivalence and order relations, which have been evaluated with matching-to-sample and sequence production tasks, respectively. Based on the requirements of such tasks, we suggest an account of number skill acquisition that requires integration of two kinds of stimulus classes, feature classes and arbitrary classes. Feature classes are demonstrated when it is shown that the physical features of the stimuli that define the class exert discriminative control of responding. The arbitrary classes include equivalence classes and order classes. Equivalence class formation involves establishing the mutual substitutability of stimuli that come from different feature classes (e.g., the numeral 3 and its corresponding dictated name and quantity). Order classes involve the unidirectional asymmetrical relations between the stimuli in different equivalence classes. Group and single-subject methods will be used to: (1) Assess the extent to which participants' entry competencies reflect integration of feature, equivalence, and order stimulus classes. (2) Analyze whether establishing feature and equivalence (or order) classes using quantities (1-5), corresponding spoken number names, and numerals will allow success on magnitude-comparison tasks, or whether establishing order (or equivalence) classes is also required. (3) Determine whether teaching set-construction and counting using quantities (1-10) results in equivalence classes, order classes, and magnitude judgements. (4) Examine (a) whether computer-based training can establish reliable construction of sets to "higher-order" sample stimuli requiring joint control by number and item (e.g., "two apples," "three apples," etc.) and (b) whether such training improves tabletop performances. The research has direct implications for developing effective instructional programs that establish number concepts in individuals who do not ordinarily acquire them.